Contents

Sampling variance in the Trade Union Membership Statistics ................................................... 3

Introduction on sampling variation ................................................................................................ 3

Method used to calculate confidence intervals for the Trade Union Membership Statistics ....... 3

Table 1 95% Confidence intervals for trade union membership by gender and sector ...... 5

Table 2 95% confidence intervals for trade union membership by nation and region, 2011 6

Table 3 95% confidence intervals for average (mean) employee wages, 2011, by gender and sector 7

Table 4 95% confidence intervals for trade union membership density by industry and workplace size, 2011 ................................................................................................................. 8

Table 5 95% confidence intervals for trade union membership density by occupation and age, 2011 9

Table 6 95% confidence intervals for employees with trade union presence in the workplace by sector and industry, 2011 ................................................................................................................. 10

Table 7 95% confidence intervals for employees with trade union presence in the workplace by workplace size, nation and region, 2011 ................................................................................................................. 11

Table 8 95% confidence intervals for employees whose pay and conditions are affected by a collective agreement, by sector and industry, 2011 ................................................................................................................. 12

Table 9 95% confidence intervals for employees whose pay and conditions are affected by a collective agreement, by workplace size, nation and region, 2011 ................................................................................................................. 13 Sampling variance in the Trade Union Membership Statistics

Introduction on sampling variation

The labour force survey (LFS) is a sample survey, which provides estimates of various measures of the population that reflect the particular sample selected. As any valid sample from the population is likely to produce different estimates for the population than other valid samples, there is uncertainty around the population estimates resulting from the selection of a particular sample (as opposed to any other valid sample). This is known as the sampling error. As the LFS uses random sampling of households it is possible to provide estimates of the sampling error (measured as the standard error), which forms the basis of the confidence interval placed around estimate. Normally a 95% confidence interval would be used, which means that in 19 out of 20 different samples we would expect the true (population) level or rate considered to be within the 95% confidence interval for the sample estimate. Where a simple random sample is used, the 95% confidence interval for an estimate is set at ±1.96 standard errors around the sample estimate.

Any estimate of the range of sampling variability should take into account the sampling approach, as this will affect the probability of selection of individuals within the population, and therefore the extent of the variability around the survey estimate relative to that obtained from a simple random sample. The design factor measures the ratio of the standard error produced by a complex sample design relative to the standard error that would result from simple random sampling. To take account of the sampling design, the 95% confidence interval can be calculated as:

[ \\pm 1.96 \\times \\text{design factor} \\times \\text{SE (standard error)} ]

Method used to calculate confidence intervals for the Trade Union Membership Statistics

The LFS sample design has two additional elements: implicit stratification by geography (from the use of a systematic sample of addresses based on postcode area), and clustering, based on collecting results for individuals based on a sample of addresses (as individuals within a household are more likely to share some characteristics). Some calculated design factors for headline measures are presented in ONS’s LFS User Guide, Volume 1 – LFS Background and Methodology 2011(^1). However, these do not directly relate to the estimates of trade union membership.

(^1) [http://www.ons.gov.uk/ons/guide-method/method-quality/specific/labour-market/labour-market-statistics/volume-1---2011.pdf](http://www.ons.gov.uk/ons/guide-method/method-quality/specific/labour-market/labour-market-statistics/volume-1---2011.pdf) In the methodology user guide, ONS advise that users can calculate their own confidence intervals by estimating their own design factors by applying a ‘complex samples’ analysis in a statistical package. These will be ‘conservative’ because while such an approach will take account of the LFS’s design, it won’t take account of the calibration weighting that ONS undertakes to ensure estimates are consistent across those groups calibrated on, thus reducing the standard errors.

We have estimated standard errors and confidence intervals for the 2011 estimates of trade union membership using a complex samples approach in SPSS. The address variable, ADD, has been used as the cluster variable, in line with ONS’s suggestion, and UALA, representing unitary and local authorities, has been used as a stratum variable.

The calculated 95% confidence intervals for the key trade union membership levels and density estimates for 2011 presented in the latest trade union membership publication (for 2011). The tables present the estimate, and the upper and lower bounds of the estimate at 95% confidence. If the confidence intervals of two estimated values do not overlap then they are considered statistically significantly different at the 5% significance level. Confidence intervals will be provided for all the 2012 figures provided in this year’s bulletin when it is published in April.

If you have any comments or would like further information, please contact us at:

Labourmarket.analysis@bis.gsi.gov.uk Table 1 95% Confidence intervals for trade union membership by gender and sector

| Trade union membership, 2011 | 95% confidence interval | |-----------------------------|-------------------------| | | population estimate | lower bound | Upper bound | | in employment, UK | | | | | whole economy | numbers (000s) | | | | all | 6,665 | 6,282 | 7,048 | | men | 3,089 | 2,897 | 3,281 | | women | 3,577 | 3,365 | 3,789 | | whole economy | density % | | | | all | 23.2% | 22.7% | 23.7% | | men | 20.2% | 19.5% | 20.9% | | women | 26.8% | 26.1% | 27.5% | | employees, UK | | | | | whole economy | numbers (000s) | | | | all | 6,389 | 6,022 | 6,756 | | men | 2,913 | 2,731 | 3,096 | | women | 3,476 | 3,270 | 3,681 | | public sector | | | | | all | 3,882 | 3,654 | 4,110 | | men | 1,299 | 1,209 | 1,389 | | women | 2,583 | 2,427 | 2,739 | | private sector | | | | | all | 2,507 | 2,343 | 2,671 | | men | 1,614 | 1,499 | 1,729 | | women | 893 | 824 | 962 | | whole economy | density % | | | | all | 26.0% | 25.4% | 26.6% | | men | 23.4% | 22.6% | 24.2% | | women | 28.7% | 28.0% | 29.4% | | public sector | | | | | all | 56.5% | 55.5% | 57.6% | | men | 55.4% | 53.6% | 57.2% | | women | 57.1% | 55.8% | 58.4% | | private sector | | | | | all | 14.1% | 13.6% | 14.7% | | men | 15.9% | 15.2% | 16.7% | | women | 11.8% | 11.2% | 12.4% | Table 2 95% confidence intervals for trade union membership by nation and region, 2011

| Trade union membership, 2011 | 95% confidence interval | |-----------------------------|-------------------------| | | population estimate | lower bound | upper bound | | | numbers (000s) | | | | Employees | | | | | Nation | | | | | England | 5,125 | 4,784 | 5,466 | | Wales | 400 | 302 | 499 | | Scotland | 638 | 548 | 728 | | Northern Ireland | 226 | 190 | 262 | | Regions | | | | | North East | 341 | 257 | 425 | | North West | 825 | 668 | 983 | | Yorkshire & Humberside | 555 | 463 | 647 | | East Midlands | 456 | 342 | 569 | | West Midlands | 550 | 443 | 656 | | East of England | 535 | 404 | 666 | | London | 636 | 568 | 705 | | South East | 719 | 581 | 856 | | South West | 509 | 407 | 610 | | density % | | | | | Nation | | | | | England | 24.8% | 24.2% | 25.4% | | Wales | 34.9% | 32.3% | 37.6% | | Scotland | 29.8% | 28.0% | 31.7% | | Northern Ireland | 33.6% | 31.4% | 35.9% | | Regions | | | | | North East | 34.2% | 31.6% | 36.8% | | North West | 30.3% | 28.7% | 31.9% | | Yorkshire & Humberside | 27.0% | 25.3% | 28.7% | | East Midlands | 25.4% | 23.4% | 27.5% | | West Midlands | 26.6% | 24.9% | 28.4% | | East of England | 22.4% | 20.9% | 23.9% | | London | 20.6% | 19.1% | 22.1% | | South East | 20.7% | 19.4% | 22.2% | | South West | 24.7% | 22.9% | 26.6% | Table 3 95% confidence intervals for average (mean) employee wages, 2011, by gender and sector

Mean hourly earnings (£), 2011

| UK employees | 95% confidence interval | |--------------|-------------------------| | | Estimate | lower bound | higher bound | | whole economy | | | | | all employees | £12.60 | £12.39 | £12.81 | | trade union members | £14.18 | £13.92 | £14.44 | | non-members | £12.01 | £11.75 | £12.27 |

by sector

public sector

| all employees | £14.11 | £13.83 | £14.38 | | trade union members | £15.06 | £14.74 | £15.39 | | non-members | £12.76 | £12.30 | £13.22 |

private sector

| all employees | £12.03 | £11.77 | £12.29 | | trade union members | £12.83 | £12.42 | £13.25 | | non-members | £11.88 | £11.58 | £12.18 |

by gender

male

| all employees | £13.74 | £13.44 | £14.04 | | trade union members | £14.72 | £14.32 | £15.12 | | non-members | £13.40 | £13.03 | £13.77 |

female

| all employees | £11.43 | £11.23 | £11.64 | | trade union members | £13.73 | £13.43 | £14.03 | | non-members | £10.50 | £10.25 | £10.76 | Table 4 95% confidence intervals for trade union membership density by industry and workplace size, 2011

| Trade union membership, 2011 | UK employees | 95% confidence interval | |-----------------------------|--------------|-------------------------| | | population estimate | lower bound | upper bound | | by industry | density, % | | | | Agriculture, forestry & fishing | * | * | * | | Mining & quarrying | 23.5% | 16.8% | 31.9% | | Manufacturing | 18.7% | 17.2% | 20.2% | | Electricity, gas, steam & air conditioning supply | 43.2% | 37.1% | 49.6% | | Water supply, sewerage, waste & remediation activities | 28.7% | 23.7% | 34.3% | | Construction | 14.8% | 13.1% | 16.6% | | Wholesale, retail trade and motor repair | 11.9% | 10.9% | 12.9% | | Transport and storage | 38.9% | 36.3% | 41.5% | | Accommodation & food service | 3.6% | 2.8% | 4.6% | | Information & communication | 11.7% | 9.9% | 13.8% | | Financial & insurance activities | 16.7% | 14.8% | 18.9% | | Real estate activities | 12.8% | 9.0% | 18.0% | | Professional & administrative services | 10.4% | 9.3% | 11.5% | | Public administration and defence | 53.4% | 51.2% | 55.5% | | Education | 51.5% | 49.8% | 53.1% | | Human health & social work | 41.4% | 40.0% | 42.9% | | Other services | 13.6% | 11.9% | 15.6% | | by workplace size | | | | | Less than 50 | 16.3% | 15.7% | 17.0% | | 50 or more | 34.9% | 34.1% | 35.8% | Table 5 95% confidence intervals for trade union membership density by occupation and age, 2011

| Trade union membership, 2011 | population estimate | 95% confidence interval | |-----------------------------|---------------------|-------------------------| | | density, % | lower bound | upper bound | | by occupation | | | | | Managers and senior officials| 13.8% | 12.6% | 15.1% | | Professional occupations | 45.4% | 44.0% | 46.7% | | Associate professional and technical occupations | 25.7% | 24.4% | 27.1% | | Administrative and secretarial occupations | 21.2% | 19.9% | 22.5% | | Skilled trade occupations | 20.1% | 18.5% | 21.7% | | Personal service occupations | 28.0% | 26.5% | 29.5% | | Sales and customer service occupations | 15.5% | 14.2% | 16.9% | | Process, plant and machine operatives | 28.6% | 26.5% | 30.7% | | Elementary occupations | 16.7% | 15.5% | 17.9% | | by age | | | | | 16-19 | 3.1% | 2.2% | 4.3% | | 20-24 | 11.4% | 10.2% | 12.7% | | 25-29 | 18.2% | 16.9% | 19.6% | | 30 to 34 | 24.0% | 22.5% | 25.5% | | 35 to 39 | 26.7% | 25.3% | 28.2% | | 40 to 44 | 29.4% | 28.1% | 30.8% | | 45 to 49 | 33.6% | 32.1% | 35.2% | | 50 to 54 | 36.2% | 34.6% | 37.8% | | 55 to 59 | 35.3% | 33.6% | 37.0% | | 60 to 64 | 29.1% | 27.0% | 31.3% | | 65-69 | 14.1% | 11.7% | 17.0% | | Over 70 | 13.5% | 8.4% | 21.0% | Table 6 95% confidence intervals for employees with trade union presence in the workplace by sector and industry, 2011

Employees with trade union presence in the workplace, 2011

| UK employees, % | Estimate | lower bound | higher bound | |-----------------|----------|-------------|--------------| | all | 44.8% | 44.1% | 45.5% | | public sector | 87.1% | 86.3% | 87.8% | | private sector | 28.5% | 27.8% | 29.2% |

by industry

| Industry | Estimate | lower bound | higher bound | |-----------------------------------------------|----------|-------------|--------------| | Agriculture, forestry and fishing | * | * | * | | Mining and quarrying | 39.3% | 31.8% | 47.4% | | Manufacturing | 38.1% | 36.2% | 40.0% | | Electricity, gas and steam & air conditioning supply | 65.6% | 59.3% | 71.5% | | Water supply, sewerage, waste & remediation activities | 56.4% | 50.7% | 62.0% | | Construction | 27.3% | 25.2% | 29.5% | | Wholesale, retail and motor trade | 26.9% | 25.5% | 28.3% | | Transport, storage | 58.7% | 56.0% | 61.4% | | accommodation and food services | 7.6% | 6.4% | 8.9% | | information and communications | 23.8% | 21.2% | 26.5% | | Financial and insurance activities | 39.7% | 36.9% | 42.6% | | Real estate services | 35.6% | 29.9% | 41.7% | | Professional & administrative services | 21.0% | 19.6% | 22.5% | | Public admin and defence | 84.0% | 82.3% | 85.6% | | Education | 82.1% | 80.8% | 83.3% | | Health and social work | 63.3% | 61.9% | 64.8% | | Other services | 27.2% | 24.8% | 29.7% |

Note: this table provides estimates for industry based on SIC 2007, and so is slightly different for some industries than in table 3.8 in the 2011 publication. Table 7 95% confidence intervals for employees with trade union presence in the workplace by workplace size, nation and region, 2011

Employees with trade union presence in the workplace, 2011

| by workplace size | UK employees, % | 95% confidence interval | |-------------------|-----------------|-------------------------| | Less than 50 | 26.7% | 26.0% 27.5% | | 50 or more | 61.6% | 60.7% 62.5% |

| Nation | | | |-------------------|------------------|-------------------------| | England | 44.0% | 43.3% 44.7% | | Wales | 55.8% | 52.4% 59.2% | | Scotland | 48.1% | 46.1% 50.0% | | Northern Ireland | 41.8% | 38.8% 44.8% |

| Region | | | |-------------------|------------------|-------------------------| | North East | 53.5% | 50.5% 56.4% | | North West | 48.9% | 47.1% 50.6% | | Yorkshire and the Humber | 47.5% | 45.5% 49.5% | | East Midlands | 44.7% | 42.6% 46.9% | | West Midlands | 45.4% | 43.8% 47.0% | | East of England | 41.0% | 39.4% 42.7% | | London | 38.0% | 36.1% 40.0% | | South East | 40.4% | 38.7% 42.2% | | South West | 45.7% | 43.8% 47.6% | Table 8 95% confidence intervals for employees whose pay and conditions are affected by a collective agreement, by sector and industry, 2011

Employees whose pay and conditions are affected by a collective agreement, 2011

| UK employees, % | 95% confidence interval | |-----------------|-------------------------| | | Estimate | lower bound | higher bound | | all | 31.2% | 30.6% | 31.8% | | public sector | 67.8% | 66.7% | 68.8% | | private sector | 16.9% | 16.4% | 17.5% |

by industry

| Industry | Estimate | lower bound | higher bound | |-----------------------------------------------|----------|-------------|--------------| | Agriculture, forestry and fishing | * | * | * | | Mining and quarrying | 22.0% | 15.5% | 30.3% | | Manufacturing | 23.2% | 21.6% | 25.0% | | Electricity, gas and steam & air conditioning supply | 50.9% | 43.8% | 58.1% | | Water supply, sewerage, waste & remediation activities | 39.6% | 34.0% | 45.4% | | Construction | 18.0% | 16.0% | 20.2% | | Wholesale, retail and motor trade | 16.0% | 14.9% | 17.3% | | Transport, storage | 47.3% | 44.5% | 50.2% | | accommodation and food services | 4.6% | 3.7% | 5.9% | | information and communications | 13.9% | 11.9% | 16.2% | | Financial and insurance activities | 25.0% | 22.4% | 27.8% | | Real estate services | 19.0% | 14.1% | 25.2% | | Professional & administrative services | 11.6% | 10.5% | 12.9% | | Public admin and defence | 71.1% | 68.9% | 73.1% | | Education | 59.0% | 57.2% | 60.8% | | Health and social work | 43.8% | 42.2% | 45.4% | | Other services | 17.5% | 15.4% | 19.7% |

Note: this table provides estimates for industry based on SIC 2007, and so is slightly different for some industries than in tables 3.8 and 3.9 in the 2011 publication. Table 9 95% confidence intervals for employees whose pay and conditions are affected by a collective agreement, by workplace size, nation and region, 2011

Employees whose pay and conditions are affected by a collective agreement, 2011

| UK employees, % | 95% confidence interval | |-----------------|-------------------------| | | Estimate | lower bound | higher bound | | **by workplace size** | | | | | Less than 50 | 17.3% | 16.6% | 18.0% | | 50 or more | 44.1% | 43.2% | 45.0% | | **Nation** | | | | | England | 30.0% | 29.3% | 30.7% | | Wales | 39.2% | 35.6% | 43.0% | | Scotland | 34.7% | 32.8% | 36.5% | | Northern Ireland| 40.6% | 37.4% | 43.9% | | **Region** | | | | | North East | 35.8% | 32.8% | 38.8% | | North West | 34.6% | 33.0% | 36.2% | | Yorkshire and the Humber | 31.8% | 29.9% | 33.8% | | East Midlands | 31.1% | 29.2% | 33.0% | | West Midlands | 33.3% | 31.3% | 35.5% | | East of England | 28.1% | 26.1% | 30.2% | | London | 24.2% | 22.6% | 26.0% | | South East | 26.6% | 24.8% | 28.5% | | South West | 31.3% | 29.7% | 32.9% | | **by gender** | | | | | Male | 28.4% | 27.6% | 29.3% | | Female | 34.0% | 33.2% | 34.8% | | **by union membership** | | | | | Member | 73.2% | 72.2% | 74.2% | | Non-member | 15.5% | 15.0% | 16.1% |